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41
Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics, and Computation
 Information and Computation
, 1997
"... Disjunctive logic programs have become a powerful tool in knowledge representation and commonsense reasoning. This paper focuses on stable model semantics, currently the most widely acknowledged semantics for disjunctive logic programs. After presenting a new notion of unfounded sets for disjunct ..."
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Cited by 88 (20 self)
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Disjunctive logic programs have become a powerful tool in knowledge representation and commonsense reasoning. This paper focuses on stable model semantics, currently the most widely acknowledged semantics for disjunctive logic programs. After presenting a new notion of unfounded sets for disjunctive logic programs, we provide two declarative characterizations of stable models in terms of unfounded sets. One shows that the set of stable models coincides with the family of unfoundedfree models (i.e., a model is stable iff it contains no unfounded atoms). The other proves that stable models can be defined equivalently by a property of their false literals, as a model is stable iff the set of its false literals coincides with its greatest unfounded set. We then generalize the wellfounded WP operator to disjunctive logic programs, give a fixpoint semantics for disjunctive stable models and present an algorithm for computing the stable models of functionfree programs. The algor...
Negation As Failure In The Head
, 1998
"... The class of logic programs with negation as failure in the head is a subset of the logic of MBNF introduced by Lifschitz and is an extension of the class of extended disjunctive programs. An interesting feature of such programs is that the minimality of answer sets does not hold. This paper conside ..."
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Cited by 67 (2 self)
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The class of logic programs with negation as failure in the head is a subset of the logic of MBNF introduced by Lifschitz and is an extension of the class of extended disjunctive programs. An interesting feature of such programs is that the minimality of answer sets does not hold. This paper considers the class of {\em general extended disjunctive programs\/} (GEDPs) as logic programs with negation as failure in the head. First, we discuss that the class of GEDPs is useful for representing knowledge in various domains in which the principle of minimality is too strong. In particular, the class of abductive programs is properly included in the class of GEDPs. Other applications include the representation of inclusive disjunctions and circumscription with fixed predicates. Secondly, the semantic nature of GEDPs is analyzed by the syntax of programs. In acyclic programs, negation as failure in the head can be shifted to the body without changing the answer sets of the program. On the other hand, supported sets of any program are always preserved by the same transformation. Thirdly, the computational complexity of the class of GEDPs is shown to remain in the same complexity class as normal disjunctive programs. Through the simulation of negation as failure in the head, computation of answer sets and supported sets is realized using any proof procedure for extended or positive disjunctive programs. Finally, a simple translation of GEDPs into autoepistemic logic is presented.
Logic and Databases: a 20 Year Retrospective
, 1996
"... . At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire ..."
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Cited by 58 (1 self)
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. At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire and Nicolas in Toulouse, France, which culminated in a workshop held in Toulouse, France in 1977. It is appropriate, then to provide an assessment as to what has been achieved in the twenty years since the field started as a distinct discipline. In this retrospective I shall review developments that have taken place in the field, assess the contributions that have been made, consider the status of implementations of deductive databases and discuss the future of work in this area. 1 Introduction As described in [234], the use of logic and deduction in databases started in the late 1960s. Prominent among the developments was the work by Levien and Maron [202, 203, 199, 200, 201] and Kuhns [1...
Prioritized Logic Programming and Its Application to Commonsense Reasoning
, 2000
"... Representing and reasoning with priorities are important in commonsense reasoning. This paper introduces a framework of prioritized logic programming (PLP), which has a mechanism of explicit representation of priority information in a program. When a program contains incomplete or indefinite informa ..."
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Cited by 52 (1 self)
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Representing and reasoning with priorities are important in commonsense reasoning. This paper introduces a framework of prioritized logic programming (PLP), which has a mechanism of explicit representation of priority information in a program. When a program contains incomplete or indefinite information, PLP is useful for specifying preference to reduce nondeterminism in logic programming. Moreover, PLP can realize various forms of commonsense reasoning in AI such as abduction, default reasoning, circumscription, and their prioritized variants. The proposed framework increases the expressive power of logic programming and exploits new applications in knowledge representation. Keywords: prioritized logic programs, abduction, default reasoning, prioritized circumscription 1 Introduction In commonsense reasoning a theory is usually assumed incomplete and may contain indefinite or conflicting knowledge. Under such circumstances, priority information is useful to select appropriate know...
Abducing through negation as failure: stable models within the independent choice logic
 J. Log. Program
"... The independent choice logic (ICL) is part of a project to combine logic and decision/game theory into a coherent framework. The ICL has a simple possibleworlds semantics characterised by independent choices and an acyclic logic program that specifies the consequences of these choices. This paper g ..."
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Cited by 50 (8 self)
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The independent choice logic (ICL) is part of a project to combine logic and decision/game theory into a coherent framework. The ICL has a simple possibleworlds semantics characterised by independent choices and an acyclic logic program that specifies the consequences of these choices. This paper gives an abductive characterization of the ICL. The ICL is defined modeltheoretically, but we show that it is naturally abductive: the set of explanations of a proposition g is a concise description of the worlds in which g is true. We give an algorithm for computing explanations and show it is sound and complete with respect to the possibleworlds semantics. What is unique about this approach is that the explanations of the negation of g can be derived from the explanations of g. The use of probabilities over choices in this framework and going beyond acyclic logic programs are also discussed.
Preferred Answer Sets for Ordered Logic Programs
 In European Conference on Logics for Artificial Intelligence (JELIA
, 2002
"... We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a "best" answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a preference for satisfying certain rules, possibl ..."
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Cited by 34 (8 self)
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We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a "best" answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a preference for satisfying certain rules, possibly at the cost of violating less important ones. We show that such a rule order induces a natural order on extended answer sets, the minimal elements of which we call preferred answer sets. We characterize the expressiveness of the resulting semantics and show that it can simulate negation as failure as well as disjunction. We illustrate an application of the approach by considering database repairs, where minimal repairs are shown to correspond to preferred answer sets.
Induction from answer sets in nonmonotonic logic programs
 ACM Transactions on Computational Logic
"... Inductive logic programming (ILP) realizes inductive machine learning in computational logic. However, the present ILP mostly handles classical clausal programs, especially Horn logic programs, and has limited applications to learning nonmonotonic logic programs. This article studies a method for re ..."
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Cited by 12 (0 self)
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Inductive logic programming (ILP) realizes inductive machine learning in computational logic. However, the present ILP mostly handles classical clausal programs, especially Horn logic programs, and has limited applications to learning nonmonotonic logic programs. This article studies a method for realizing induction in nonmonotonic logic programs. We consider an extended logic program as a background theory, and introduce techniques for inducing new rules using answer sets of the program. The produced new rules explain positive/negative examples in the context of inductive logic programming. The proposed methods extend the present ILP techniques to a syntactically and semantically richer framework, and contribute to a theory of nonmonotonic ILP.
Abducing Priorities to Derive Intended Conclusions
 In Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence (IJCAI’99
, 1999
"... inouefieedept.kobeu.ac.jp We introduce a framework for finding preference information to derive desired conclusions in nonmonotonic reasoning. A new abductive framework called preference abduction enables us to infer an appropriate set of priorities to explain the given observation skeptically, the ..."
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Cited by 9 (1 self)
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inouefieedept.kobeu.ac.jp We introduce a framework for finding preference information to derive desired conclusions in nonmonotonic reasoning. A new abductive framework called preference abduction enables us to infer an appropriate set of priorities to explain the given observation skeptically, thereby resolving the multiple extension problem in the answer set semantics for extended logic programs. Preference abduction is also combined with a usual form of abduction in abductive logic programming, and has applications such as specification of rule preference in legal reasoning and preference view update. The issue of learning abducibles and priorities is also discussed, in which abduction to a particular cause is equivalent to abduction to preference. 1
Abductive Logic Programming with Tabled Abduction
"... Abstract—In abductive logic programming, abductive solutions are typically computed without attending to the abductive context. These abductive solutions can actually be reused in a different abductive context. In this paper, we employ a tabling mechanism and propose a tabled abduction mechanism, th ..."
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Cited by 8 (8 self)
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Abstract—In abductive logic programming, abductive solutions are typically computed without attending to the abductive context. These abductive solutions can actually be reused in a different abductive context. In this paper, we employ a tabling mechanism and propose a tabled abduction mechanism, that consists of a transformation from abductive normal logic programs into tabled dual programs, by tabling abductive solution entries and without requiring any metainterpreter. Recomputation of abductive solutions for a different context, but consistent with them, can then be avoided, by reusing the tabled abductive solution entries. Though our implementation is in XSBProlog, its concepts may be imported to other systems, not necessarily Logic Programming ones. Keywordstabled abduction; abduction transformation; wellfounded semantics; XSBProlog. I.
Specifying Transactions for Extended Abduction
 In: Proc. 14th Int'l Joint Conf. on Artificial Intelligence
, 1998
"... Extended abduction introduced by Inoue and Sakama (1995) generalizes traditional abduction in the sense that it can compute negative explanations by removing hypotheses from a nonmonotonic background theory, rather than only adding them. Also, it has a mechanism of computing antiexplanations ..."
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Cited by 8 (3 self)
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Extended abduction introduced by Inoue and Sakama (1995) generalizes traditional abduction in the sense that it can compute negative explanations by removing hypotheses from a nonmonotonic background theory, rather than only adding them. Also, it has a mechanism of computing antiexplanations to unexplain negative observations. Such extended abduction not only enhances reasoning ability of traditional abduction but has useful applications to nonmonotonic theory change. In this paper, we study the computational aspect of extended abduction. Given a background theory written in nonmonotonic logic programming, we introduce its transaction program for computing extended abduction. A transaction program is a set of nondeterministic production rules that specify addition and deletion of abductive hypotheses. Abductive explanations are computed by the fixpoint of a transaction program using a bottomup model generation procedure. In the context of databases, a transactio...